Question: A group of adults and kids went to see a movie. Tickets cost $$6.00$ each for adults and $$3.50$ each for kids, and the group paid $$33.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${6x+3.5y = 33}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${6}{(y-4)}{+ 3.5y = 33}$ Simplify and solve for $y$ $ 6y-24 + 3.5y = 33 $ $ 9.5y-24 = 33 $ $ 9.5y = 57 $ $ y = \dfrac{57}{9.5} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(6)}{ - 4}$ ${x = 2}$ You can also plug ${y = 6}$ into ${6x+3.5y = 33}$ and get the same answer for $x$ ${6x + 3.5}{(6)}{= 33}$ ${x = 2}$ There were $2$ adults and $6$ kids.